CN110757504A - Positioning error compensation method of high-precision movable robot - Google Patents

Positioning error compensation method of high-precision movable robot Download PDF

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CN110757504A
CN110757504A CN201910939747.6A CN201910939747A CN110757504A CN 110757504 A CN110757504 A CN 110757504A CN 201910939747 A CN201910939747 A CN 201910939747A CN 110757504 A CN110757504 A CN 110757504A
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coordinate system
robot
rod
measurement
reference surface
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CN110757504B (en
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宋宁
樊小蒲
刘咸超
郭容
郭晟
刘勇
程艳奎
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Yibin Vocational and Technical College
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Yibin Vocational and Technical College
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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J19/00—Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J19/00—Accessories fitted to manipulators, e.g. for monitoring, for viewing; Safety devices combined with or specially adapted for use in connection with manipulators
    • B25J19/02—Sensing devices
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls

Abstract

The invention discloses a positioning error compensation method of a high-precision movable robot, which comprises an X rod, a Y rod and a Z rod which are respectively positioned on X, Y, Z axes of a measurement coordinate system { M } and are intersected at an original point, wherein the X rod, the Y rod and the Z rod are respectively provided with a high-precision laser distance sensor for measuring the distance from the original point of the coordinate system to a bottom measurement reference surface 6, a left side measurement reference surface 2 and a rear side measurement reference surface 10, the bottom measurement reference surface 6 is a horizontal plane, and the left side measurement reference surface 2 and the rear side measurement reference surface 10 are two vertical planes which are vertical to each other and vertical to the bottom measurement reference surface; the invention can effectively reduce the influence of the moving positioning error on the robot.

Description

Positioning error compensation method of high-precision movable robot
Technical Field
The invention relates to the field of robots, in particular to a positioning error compensation method of a high-precision movable robot.
Background
The working state of the industrial robot is described by the position and the rotation angle of The Central Point (TCP) of the end tool relative to a base coordinate system, which is called pose for short. The process of executing program operation by the industrial robot is actually the process of switching the terminal pose of the industrial robot in different states and finishing planning actions. The programmed coordinate system can be divided into a base coordinate system, a tool coordinate system and a workpiece coordinate system, and the poses described in the workpiece coordinate system and the tool coordinate system can be converted into the poses in the base coordinate system through the transformation relation between the coordinate system and the base coordinate system.
After the mobile robot is programmed, the mobile robot enters the station again, certain errors exist in the position and the direction of the robot base when the robot base is programmed, the positioning errors cause the displacement and the rotation of the robot base coordinate system { B }, and the working accuracy of the tail end of the industrial robot is influenced finally. In order to improve the working precision of the mobile industrial robot, the robot can be physically fixed before operation, and the fixing process is secondary positioning. The secondary positioning can greatly reduce the influence caused by the positioning error of the robot, but due to the manufacturing, assembly, use abrasion and the like of the secondary positioning device, the secondary positioning also has a slight error, and the precision of the robot is influenced.
In order to improve the working precision of the mobile industrial robot, the robot can be physically fixed before operation, and the fixing process is secondary positioning. Because the industrial robot carries out physical positioning in the secondary positioning device, the secondary positioning error is measured as a micro error, and the measurement precision is objectively required to be high, the measurement is timely and quick, and the size of the measurement instrument is small. At present, the robot pose measurement method uses laser tracker measurement, theodolite measurement, three-coordinate measuring machine measurement and industrial camera shooting measurement, but the methods are not suitable for real-time measurement of robot positioning errors due to large equipment size, high cost, inconvenient operation, complex system and the like.
Therefore, it is desirable to compensate for an error generated when the robot is secondarily positioned and to correct the error generated when the robot is positioned in time.
Disclosure of Invention
The invention aims to solve the technical problems that when the existing movable robot enters a station, a positioning error is generated, and the robot cannot be corrected in time when in use, so that the working precision of the robot is influenced; the method aims to provide a method for compensating the positioning error of the high-precision movable robot and solve the problem of compensating the positioning error of the robot.
The invention is realized by the following technical scheme:
the positioning error measurement compensation method of the high-precision movable robot comprises an X rod, a Y rod and a Z rod which are respectively positioned on X, Y and Z coordinate axes of a measurement coordinate system { M } and are intersected at an original point, wherein the X rod, the Y rod and the Z rod are respectively provided with an X ranging sensor, a Y ranging sensor and a Z ranging sensor which are respectively used for measuring the distances from the original point of the measurement coordinate system to a bottom measurement reference surface, a left side measurement reference surface and a rear side measurement reference surface; the bottom measuring reference surface, the left measuring reference surface and the rear measuring reference surface are respectively positioned on the bottom surface, the side surface and the rear side surface of the positioning device.
An X-axis horizontal tilt angle sensor and a Y-axis horizontal tilt angle sensor for measuring horizontal tilt angles of X and Y coordinate axes of a coordinate system { M } are respectively connected below the X rod and the Y rod; the X rod is also connected with a coordinate axis vertical inclination angle sensor for measuring an included angle between a zx coordinate plane and a vertical plane in a coordinate system { M } in a plane vertical to the X axis; and a magnetic field direction sensor for measuring the angular displacement of the coordinate system { M } relative to the earth magnetic field on the horizontal plane is connected to the Y rod.
The vertical tilt angle sensor of the coordinate axis comprises a connecting shaft, a balancing block and an angle sensor, wherein the balancing block and the angle sensor can rotate around the connecting shaft, the angle sensor comprises a movable end and a fixed end, the movable end is connected with the balancing block, the fixed end is connected with the connecting shaft, the connecting shaft is connected with the X rod, and the connecting shaft and the axis of the X rod are overlapped with each other.
Furthermore, the bottom measuring reference surface of the measuring device is a horizontal surface, and the left measuring reference surface and the rear measuring reference surface are two vertical surfaces which are vertical to each other and are vertical to the bottom measuring reference surface. A measurement coordinate system { M } is constructed in the space positioning error measurement device, the X-axis distance measurement probe, the Y-axis distance measurement probe and the Z-axis distance measurement probe are coaxially arranged with the X axis, the Y axis and the Z axis, and the X-axis horizontal inclination angle sensor and the Y-axis horizontal inclination angle sensor are positioned below the X axis and the Y axis and are respectively arranged in parallel with the X axis and the Y axis and are used for measuring the horizontal inclination angles of the X coordinate axis and the Y coordinate axis; the axis of the connecting shaft of the coordinate axis vertical inclination angle sensor is coincident with the x axis and is used for measuring the included angle between the zx coordinate plane and the vertical plane in the plane vertical to the x axis.
The coordinate axis vertical inclination angle sensor comprises a connecting shaft, a balance block and an angle sensor, wherein the balance block can rotate around the connecting shaft, the angle sensor comprises a movable end and a fixed end, the movable end is connected with the balance block, the fixed end is connected with the connecting shaft, the connecting shaft is connected with the X rod, and the straight line where the connecting shaft and the X rod are located coincides with each other. The sensor mainly comprises a connecting shaft, a balance block capable of rotating around a shaft and an angle sensor. The angle sensor consists of a movable end and a fixed end, wherein the movable end is connected with a balance block, and the fixed end is connected with a shaft.
In the measurement, the axis of the sensor is installed at a position coaxial with the measured coordinate axis. The inclination angle of the coordinate axis and the horizontal plane is very small because the measured error is a micro error. When the coordinate plane is not coincident with the vertical plane, under the action of gravity, the connecting line of the center of gravity and the axis of the balance weight is always kept in the vertical plane, so that the movable end and the fixed end of the angle sensor generate angular displacement, and the angular displacement is the included angle between the coordinate plane and the vertical plane.
This device is when measuring, does not have numerous and diverse structure, and the size is less, the more convenient to use, and the error of this device is also littleer simultaneously, further improvement the availability factor.
The measuring method of the space positioning error measuring device comprises the following steps:
(1) the transformation relationship of the measured coordinate system { M } with respect to the world coordinate system { W } is expressed as:
Figure BDA0002222551540000031
wherein, Tx(xM)、Ty(yM)、Tz(zM) Homogeneous matrices, R, being respectively W to M shift transformationsz(ψ)、
Figure BDA0002222551540000032
Ry″(theta) is a homogeneous matrix of { M } rotation transformations around the z-axis, the x '-axis and the y' -axis in sequence, respectively;
(2) the angle ψ, ∠ bO, through which the measurement coordinate system { M } is rotated about the z-axis is obtained by means of the magnetic field direction sensorMb′；
(3) Obtaining the angle of the measurement coordinate system (M) rotating around the x' axis through the Y-axis horizontal inclination angle sensor
Figure BDA0002222551540000039
I.e. ∠ b "OMb′；
(4) An included angle α between a zx coordinate plane and a vertical plane passing through the x axis on a plane perpendicular to the x axis is obtained through a coordinate axis vertical inclination angle sensorx(ii) a The inclination angle theta between the X axis and the horizontal plane is measured by the X axis horizontal inclination angle sensor0Through αxAnd theta0The angle θ by which the coordinate system { M } rotates around the y-axis is obtained as:
(5) the distances from the light spots on the bottom measuring reference surface, the left measuring reference surface and the rear measuring reference surface to the origin of the measuring coordinate system { M } are respectively Lx, Ly and Lz measured by the Z distance measuring sensor, the Y distance measuring sensor and the X distance measuring sensor, so that the moving distances from the world coordinate system { W } to the origin of the measuring coordinate system { M } in the directions of X, Y and Z can be calculated to be respectively Lx, Ly and Lz
Figure BDA0002222551540000034
Figure BDA0002222551540000035
Figure BDA0002222551540000036
(6) Substituting the parameters determined in the steps (2) to (5) into the calculation formula in the step (1) to obtain the position and the direction of the device relative to the world coordinate system { W }, further determining the spatial position and the direction of the robot on which the spatial positioning error measuring device is installed and the error between the measured position and direction and the correct position and direction.
Specifically, a positioning error measuring device is connected to a robot base, a measuring coordinate system { M } is arranged in the positioning error measuring device, the measuring coordinate system { M } is parallel to the robot base coordinate system { B } in direction, the relative position is fixed, and the position difference in x, y and z directions is respectively delta x, delta y and delta z; the compensation method comprises the following steps:
(1) the displacement errors in the x, y and z directions and the angle errors around the rotation x, y and z measured during the programming of the robot are respectively x0、y0、z、
Figure BDA0002222551540000037
θ0、ψ0The displacement errors in the x, y and z directions and the angular errors around the rotation x, y and z measured at this time are respectively xi、yi、zi、
Figure BDA0002222551540000038
θi、ψi：
Transformation in the new base coordinate system { B' } into the old base coordinate system { B }:
Figure BDA0002222551540000041
in the formula
Figure BDA0002222551540000042
A homogeneous transformation matrix of { B '} to { M' },
Figure BDA0002222551540000043
a homogeneous transformation matrix of { M' } to { M },
Figure BDA0002222551540000044
a homogeneous transformation matrix of { M } to { B };
wherein:
Figure BDA0002222551540000045
Figure BDA0002222551540000047
(2) and (3) converting the pose of the robot terminal coordinate system in the new base coordinate:
Figure BDA0002222551540000048
in the formula (I), the compound is shown in the specification,
Figure BDA0002222551540000049
the pose of the industrial robot in the old base coordinates.
(3) For equation (8), if it is the joint coordinate pose, it can be transformed by the following transformation relation function:
Figure BDA00022225515400000410
in the formula qiIndividual joint variables.
(4) If the pose data are rectangular coordinate pose data in the workpiece coordinate system and the tool coordinate system, the workpiece coordinate system or the tool coordinate system can be compensated according to the following calculation method, and after the workpiece coordinate system or the tool coordinate system is corrected, the robot corrects the related pose data according to the correction data.
Figure BDA00022225515400000411
Figure BDA00022225515400000412
Wherein, { T } is an end coordinate system in the base coordinate system { B }, and { M' } is a post-secondary-positioning measurement coordinate system,
Figure BDA00022225515400000413
a homogeneous transformation matrix of { B '} to { M' },
Figure BDA00022225515400000414
a homogeneous transformation matrix of { M' } to { M },
Figure BDA00022225515400000415
a homogeneous transformation matrix of { M } to { B }; i is the number of joints of the robot,
Figure BDA0002222551540000051
representing pose data of the robot end effector in base coordinates, f (q)i) Is a function of a transformation relation, wherein qiEach joint variable;
Figure BDA0002222551540000052
the transformation relations from the robot coordinate system { B } to the workpiece coordinate system { P } and the tool coordinate system { T }, respectively;
(5) the former positioning error and the current positioning error are respectively substituted into the formula (5) to obtain a homogeneous transformation matrix
Figure BDA0002222551540000053
Further calculating according to the formula (6) to obtain the productHomogeneous transformation matrix from the pre-base coordinate system { B' } to the original base coordinate system { B }
(6) According to the pose data types in the programs, respectively
Figure BDA0002222551540000055
The pose data are updated by substituting in equations (7), (8) and (9).
Compared with the prior art, the invention has the following advantages and beneficial effects:
1. the invention discloses a positioning error compensation method of a high-precision movable robot, which can effectively reduce the influence of the moving positioning error on the robot. The mathematical model of error soft compensation has no approximate algorithm and no principle error, so the effect of error correction depends on the measurement precision of positioning error;
2. according to the positioning error compensation method of the high-precision movable robot, the measurement precision of the displacement error is 1 mu m, the angle measurement precision is within 0.01 degrees, and the use efficiency is higher;
3. the method for compensating the positioning error of the high-precision movable robot is simple to operate, free of complex structure and operation, convenient to operate and use and high in use efficiency.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a schematic structural view of the present invention;
FIG. 2 is a schematic diagram of a coordinate axis vertical tilt sensor junction in accordance with the present invention;
FIG. 3 is a diagram of the transformation of the world coordinate system by rotation of the displacement of the measurement coordinate system according to the present invention;
FIG. 4 is a schematic view of the present invention illustrating the principle of measuring the rotation angle about the x-axis;
FIG. 5 illustrates the transformation of the robot coordinate system caused by the secondary positioning error according to the present invention;
FIG. 6 is a flowchart of a positioning error compensation routine of the present invention.
Reference numbers and corresponding part names in the drawings:
the method comprises the following steps of 1-a magnetic field angle sensor, 2-a left side measurement reference surface, 3-Y distance measurement probes, 4-Y axis horizontal tilt angle sensors, 5-Z distance measurement probes, 6-a bottom measurement reference surface, 7-X axis horizontal tilt angle sensors, 8-coordinate axis vertical tilt angle sensors, 9-X distance measurement probes, 10-a rear side measurement reference surface, 11-a connecting shaft, 12-an angle sensor and 13-a balance block.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not used as limitations of the present invention.
Example 1
The invention relates to a positioning error compensation method of a high-precision movable robot, which comprises an X rod, a Y rod and a Z rod which are respectively positioned on X, Y, Z axes of a measurement coordinate system { M } and intersect at an original point, wherein the X rod, the Y rod and the Z rod are respectively provided with a high-precision laser distance sensor for measuring the distance from the original point of the coordinate system to a bottom measurement reference surface 6, a left side measurement reference surface 2 and a rear side measurement reference surface 10, the bottom measurement reference surface 6 is a horizontal plane, and the left side measurement reference surface 2 and the rear side measurement reference surface 10 are two vertical planes which are vertical to each other and vertical to the bottom measurement reference surface;
an X-axis horizontal tilt angle sensor 7 and a Y-axis horizontal tilt angle sensor 4 for measuring horizontal tilt angles of X and Y coordinate axes are respectively connected below the X rod and the Y rod; the X rod is also connected with a coordinate axis vertical inclination angle sensor 8 for measuring the included angle between the zx coordinate plane and the vertical plane in the plane vertical to the X axis; the Y-pole is connected to a magnetic field direction sensor 1 that measures angular displacement in the horizontal plane of the coordinate system { M } relative to the earth's magnetic field.
As shown in fig. 2, the coordinate axis vertical tilt sensor 8 includes a connecting shaft 11, a balance weight 13 rotatable around the connecting shaft 11, and an angle sensor 12, where the angle sensor 12 includes a movable end and a fixed end, the movable end is connected to the balance weight 13, the fixed end is connected to the connecting shaft 11, the connecting shaft 11 is connected to the X-rod, and the straight lines of the connecting shaft 11 and the X-rod coincide with each other.
Wherein, the X distance measuring sensor 9, the Y distance measuring sensor 3 and the Z distance measuring sensor 5 are high-precision laser distance measuring sensors.
When the device is used, a horizontal and vertical measuring reference surface, namely the bottom measuring reference surface 6, the left measuring reference surface 2 and the rear measuring reference surface 10, is arranged on the bottom surface, the side surface and the rear side surface of the secondary positioning device, and meanwhile, the measuring reference surface is not connected with a positioning clamping device on the secondary positioning device, so that the measuring reference surface is prevented from being influenced by the vibration of the secondary positioning device.
The apparatus mounting coordinate system { M } direction is parallel to the robot base coordinate system, and the relative position is fixed, and the positional differences in the three directions x, y, and z are Δ x, Δ y, and Δ z, respectively. Wherein, Δ x, Δ y, Δ z are variable mechanical installation parameters related to the device under test, and specific values need to be measured after the measurement device is installed.
Therefore, when the device is used, the position and the direction of the device relative to the world coordinate system { W } are measured, the space position and the direction of the robot installed by the device can be obtained, and the error of the secondary positioning device is obtained by comparing the measured position and direction with the correct position and direction.
Example 2
The measuring method of the positioning error measuring device comprises the following steps based on the embodiment 1:
(1) the transformation relationship of the measured coordinate system { M } with respect to the world coordinate system { W } is expressed as:
Figure BDA0002222551540000061
wherein, Tx(xM)、Ty(yM)、Tz(zM) Homogeneous matrices, R, being respectively W to M shift transformationsz(ψ)、
Figure BDA0002222551540000071
Ry″(theta) is a homogeneous matrix of { M } rotation transformations around the z-axis, the x '-axis and the y' -axis in sequence, respectively;
Figure BDA0002222551540000072
Figure BDA0002222551540000073
Figure BDA0002222551540000074
(2) the angle ψ, ∠ bO, of the rotation of the measurement coordinate system { M } about the z-axis is obtained by means of the magnetic field direction sensor (1)Mb′；
(3) The angle of the measurement coordinate system { M } rotating around the x' axis is obtained through a Y-axis horizontal inclination angle sensor (4)
Figure BDA0002222551540000075
I.e. ∠ b "OMb′；
(4) An included angle α between a zx coordinate plane and a vertical plane passing through the x axis on a plane vertical to the x axis is obtained by a coordinate axis vertical inclination angle sensor (8)x(ii) a The inclination angle theta between the X axis and the horizontal plane is measured by an X axis horizontal inclination angle sensor (7)0Through αxAnd theta0The angle θ by which the coordinate system { M } rotates around the y-axis is obtained as:
Figure BDA0002222551540000076
(5) the distances from the light spots on the rear side measurement reference surface, the left side measurement reference surface and the bottom measurement reference surface to the origin of the measurement coordinate system { M } are Lx, Ly and Lz respectively measured by the X, Y, Z high-precision laser distance measuring sensor, and further the moving distances from the world coordinate system { W } to the origin of the measurement coordinate system { M } in the directions of x, y and z can be calculated to be Lx, Ly and Lz respectively
Figure BDA0002222551540000078
Figure BDA0002222551540000079
(6) Substituting the parameters determined in steps (2) - (5) into the calculation formula in step (1) can determine the position and orientation of the spatial positioning error measurement device of claim 1 with respect to the world coordinate system { W }, and can further determine the spatial position and orientation of the device on which the spatial positioning error measurement device is mounted, and the error between the measured position and orientation and the correct position and orientation.
Example 3
On the basis of embodiment 2, the mobile robot enters the station twice before and after, and due to hardware positioning, a certain error exists before and after the position and the direction of the robot base, which actually causes the displacement and the rotation of the robot base coordinate system { B }. For any one working state, the robot end and the robot base body can be regarded as rigid bodies, therefore, the base coordinate changes, and the end coordinate system { T } in the base coordinate system follows the same displacement and rotation to { T' }, as shown in FIG. 5.
To eliminate the influence of the secondary positioning on the pose of the robot end, the original pose end coordinate system { T } of the end needs to be represented again in the new base coordinate system { B' }.
The transformation relationship to the old base coordinate system { B } in the new base coordinate system { B '}, the transformation path from { B' } to { B } is: { B '} → { M' } → { M } → { B }. Thus, the transformation relationship:
Figure BDA0002222551540000081
in the formula
Figure BDA0002222551540000082
A homogeneous transformation matrix of { B '} to { M' },
Figure BDA0002222551540000083
a homogeneous transformation matrix of { M' } to { M },is a homogeneous transformation matrix of { M } to { B }.
Figure BDA0002222551540000085
Figure BDA0002222551540000086
The displacement errors in the x, y and z directions and the angle errors around the rotation x, y and z measured by the robot for the first time are respectively x0、y0、z、θ0、ψ0The displacement errors in the x, y and z directions and the angle errors around the rotation x, y and z measured at this time are x, y and z respectivelyi、yi、zi、
Figure BDA0002222551540000088
θi、ψiThen the position relationship between the new measurement coordinate system { M' } and the old measurement coordinate system { M } can be expressed as
Figure BDA0002222551540000089
Then
Figure BDA00022225515400000810
The fact that the rectangular coordinate pose data of the industrial robot end is described by conversion is that the robot base coordinate system { B } is converted into the end coordinate system { i }, if the pose is used
Figure BDA00022225515400000811
Indicating that, after applying the positioning error compensation, the relationship between { B' } and { i } is
Figure BDA00022225515400000812
And (9) describing the pose of the robot end coordinate system in the new base coordinate.
Knowing the joint coordinate pose parameters, the corresponding rectangular coordinate pose data can be obtained according to a robot dynamic model, and the calculation formula is
Figure BDA0002222551540000091
Wherein i is the number of joints of the robot,
Figure BDA0002222551540000092
representing pose data of the robot end effector in base coordinates, f (q)i) To transform a function of the relationship, which is robot-specific, where qiIndividual joint variables.
After the joint coordinate pose data are converted into rectangular coordinate pose data, error compensation conversion calculation can be carried out according to the rectangular coordinate pose data.
The rectangular coordinate pose data in the workpiece coordinate system and the tool coordinate system are firstly converted into rectangular coordinate data in base coordinates by a robot built-in program before the robot executes actions, and then each joint parameter is converted according to a reverse dynamics principle. Therefore, for the compensation of the pose data of the rectangular coordinates in the workpiece coordinate system and the tool coordinate system, the pose of the workpiece coordinate system and the pose of the tool coordinate system are changed only through compensation, and the running parameters corresponding to the pose data can be automatically updated when the robot program runs. If it isFrom the robot coordinate system { B } to the workpiece coordinate system { P } and the tool coordinates, respectivelyThe transformation of the system { T }, the transformation of { B' } to the workpiece coordinate system { P } and the tool coordinate system { T } may be expressed as
Figure BDA0002222551540000094
Figure BDA0002222551540000095
After the workpiece coordinate system and the tool coordinate system are reset, the built-in robot program automatically solves the representation of the pose data in the new workpiece coordinate system and the tool coordinate system in the new base coordinate system and the corresponding joint coordinate parameters.
Example 4
For the teaching programming robot, the displacement errors of the robot in the x, y and z directions and the angle errors of the robot around the rotation x, y and z are respectively x0、y0、z、θ0、ψ0The displacement error in the x, y and z directions and the angle error around the rotation x, y and z are measured at each time as xi、yi、zi、
Figure BDA0002222551540000097
θi、ψiIn the formula (7),
and then further press
Figure BDA0002222551540000098
Calculating to obtain the homogeneous transformation matrix from the current base coordinate system { B' } to the original base coordinate system { B }
Figure BDA0002222551540000099
According to the pose data types in the programs, respectively
Figure BDA00022225515400000910
Substituted type (9) (10) (11)And updating pose data so as to realize the compensation of the positioning error.
For an offline programmed robot, the default raw positioning error is x0＝Cx、y0＝Cy、z0＝Cz、
Figure BDA00022225515400000911
θ0＝0°、 ψ0＝0°(Cx、Cy、CzAs a measurement constant). When the industrial robot enters the station, the front positioning errors x ', y ', z ' are measured,
Figure BDA0002222551540000101
and theta ', psi' can update the pose data in the program according to the method to perform positioning error compensation.
The positioning error compensation is realized by a program, and the principle flow of the program is shown in fig. 6. After the robot is in position each time, a copy of a program which is previously compiled is copied as a program which runs at the time, then positioning error compensation calculation is carried out, and pose data in the program are refreshed. The robot then recalculates the joint motion parameters based on the inverse kinematics and executes the modified program. After the action is executed, the program copy generated this time is useless, that is, deleted.
The above-mentioned embodiments, objects, technical solutions and advantages of the present invention are further described in detail, it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (3)

1. The method for compensating the positioning error of the high-precision movable robot is characterized in that a positioning error measuring device is connected to a robot base, a measuring coordinate system { M } is arranged in the positioning error measuring device, the measuring coordinate system { M } is parallel to a robot base coordinate system { B } in direction, the relative position is fixed, and the position differences in the x, y and z directions are respectively delta x, delta y and delta z; the compensation method comprises the following steps:
(1) the displacement errors in the x, y and z directions and the angle errors around the rotation x, y and z measured by the robot for the first time are respectively x0、y0、z、
Figure FDA0002222551530000011
θ0、ψ0The displacement errors in the x, y and z directions and the angle errors around the rotation x, y and z measured at this time are x, y and z respectivelyi、yi、zi、
Figure FDA0002222551530000012
θi、ψi：
Transformation in the new base coordinate system { B' } into the old base coordinate system { B }:
in the formula
Figure FDA0002222551530000014
A homogeneous transformation matrix of { B '} to a new measurement coordinate system of { M' },
Figure FDA0002222551530000015
a homogeneous transformation matrix of { M' } to the immediate measurement coordinate system { M },
Figure FDA0002222551530000016
a homogeneous transformation matrix of { M } to { B };
wherein:
Figure FDA0002222551530000017
Figure FDA0002222551530000018
Figure FDA0002222551530000019
(2) and (3) converting the pose of the robot terminal coordinate system in the new base coordinate:
Figure FDA00022225515300000110
in the formula (I), the compound is shown in the specification,
Figure FDA00022225515300000111
for the pose of an industrial robot in old base coordinates
(3) For equation (3), if it is the joint coordinate pose, it can be transformed by the following transformation relation function:
Figure FDA00022225515300000112
in the formula qiEach joint variable i is a robot joint sequence number;
(4) if the pose data are the pose data in the workpiece coordinate system and the tool coordinate system, the workpiece coordinate system or the tool coordinate system can be compensated according to the following calculation method, and the pose data are corrected by the robot after the workpiece coordinate system or the tool coordinate system is corrected;
Figure FDA0002222551530000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002222551530000023
is a homogeneous transformation matrix from { B '} to the new measurement coordinate system { M' },is a homogeneous transformation matrix of { M' } to the old measurement coordinate system { M },
Figure FDA0002222551530000025
a homogeneous transformation matrix of { M } to { B };
Figure FDA0002222551530000026
the transformation relations from the robot coordinate system { B } to the workpiece coordinate system { P } and the tool coordinate system { T }, respectively;
(5) respectively substituting the previous positioning error and the current positioning error into a formula (1) to obtain a homogeneous transformation matrix
Figure FDA0002222551530000027
Further calculating according to the formula (2), and obtaining a homogeneous transformation matrix from the current base coordinate system { B' } to the original base coordinate system { B }
Figure FDA0002222551530000028
(6) According to the pose data types in the programs, respectively
Figure FDA0002222551530000029
And substituting the pose data into the formulas (3), (4) and (5) to update the pose data.
2. The method of claim 1, wherein the positioning error measurement device comprises an X rod, a Y rod, and a Z rod located on the X, Y, and Z coordinate axes of the measurement coordinate system { M } and intersecting the origin, the X rod, the Y rod, and the Z rod are respectively provided with an X distance measurement sensor (9), a Y distance measurement sensor (3), and a Z distance measurement sensor (5), the Y distance measurement sensor (3), and the X distance measurement sensor (9) are respectively used to measure the distance from the origin of the measurement coordinate system to the bottom measurement reference surface (6), the left measurement reference surface (2), and the rear measurement reference surface (10), wherein the bottom measurement reference surface (6), the left measurement reference surface (2), and the rear measurement reference surface (10) respectively represent the xy plane, the X plane, the Y rod, and the Z rod of the world coordinate system { W } An xz plane and a zy plane;
an X-axis horizontal inclination angle sensor (7) and a Y-axis horizontal inclination angle sensor (4) which are used for measuring horizontal inclination angles of X and Y coordinate axes of a coordinate system { M } are respectively connected to the lower parts of the X rod and the Y rod; the X rod is also connected with a coordinate axis vertical inclination angle sensor (8) used for measuring an included angle between a zx coordinate plane and a vertical plane in a coordinate system { M } in a plane vertical to the X axis; a magnetic field direction sensor (1) for measuring the angular displacement of the coordinate system { M } relative to the earth magnetic field on the horizontal plane is connected to the Y-pole.
3. The method of compensating for the positioning error of a high-precision mobile robot according to claim 2, wherein the coordinate axis vertical tilt sensor (8) includes a connecting shaft (11), a weight (13) rotatable about the connecting shaft (11), and an angle sensor (12), the angle sensor (12) includes a movable end and a fixed end, the movable end is connected to the weight (13), the fixed end is connected to the connecting shaft (11), the connecting shaft (11) is connected to the X-pole, and the axes of the connecting shaft (11) and the X-pole coincide with each other.
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